As a workaround, if you go to your notifications inbox page, near the top right of the content area there is a little "feed" icon. It is a link to a private RSS feed to your notifications. You can use an RSS reader like a standalone application or a browser plugin to monitor. You can get a notification that way.
Above instructions are for the default lemmy interface as it appears on desktop. You can't find the link in some other interfaces. And kbin doesn't have notification inbox at all that I can find.